document.write( "Question 133099: The hypotenuse of a right triangle is 6 inches longer than the shortest side and 3 inches longer than the remaining side. Find the dimensions of the triangle. \n" ); document.write( "

Algebra.Com's Answer #97369 by vleith(2983) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let the shortest side = s. Then the hypotenuse is (s+6) and the other side is (s+6)-3 = (s+3)\r
\n" ); document.write( "\n" ); document.write( "Using the Pythagorean theorem, $\"s%5E2+%2B+%28s%2B3%29%5E2+=+%28s%2B6%29%5E2\"$
\n" ); document.write( "So:
\n" ); document.write( " $\"s%5E2+%2B+s%5E2%2B6s+%2B9+=+s%5E2+%2B+12s+%2B36\"$
\n" ); document.write( "collecting terms yields:
\n" ); document.write( " $\"s%5E2+-6s+-27+=+0+\"$
\n" ); document.write( " $\"%28s-9%29%28s%2B3%29+=+0+\"$ \r
\n" ); document.write( "\n" ); document.write( "Thus s = 9 (since it can't be a length of -3)
\n" ); document.write( "Then the other 2 kegs are (s+3) = 12 and (s+6) = 15\r
\n" ); document.write( "\n" ); document.write( "Check your answer.
\n" ); document.write( "Is 9^2 + 12^2 = 15^2? yes it is! \n" ); document.write( "

\n" );